8,487 research outputs found
Distributional fixed point equations for island nucleation in one dimension: a retrospective approach for capture zone scaling
The distributions of inter-island gaps and captures zones for islands
nucleated on a one-dimensional substrate during submonolayer deposition are
considered using a novel retrospective view. This provides an alternative
perspective on why scaling occurs in this continuously evolving system.
Distributional fixed point equations for the gaps are derived both with and
without a mean field approximation for nearest neighbour gap size correlation.
Solutions to the equations show that correct consideration of fragmentation
bias justifies the mean field approach which can be extended to provide
closed-from equations for the capture zones. Our results compare favourably to
Monte Carlo data for both point and extended islands using a range of critical
island size . We also find satisfactory agreement with theoretical
models based on more traditional fragmentation theory approaches.Comment: 9 pages, 7 figures and 1 tabl
Automated Problem Decomposition for the Boolean Domain with Genetic Programming
Researchers have been interested in exploring the regularities and modularity of the problem space in genetic programming (GP) with the aim of decomposing the original problem into several smaller subproblems. The main motivation is to allow GP to deal with more complex problems. Most previous works on modularity in GP emphasise the structure of modules used to encapsulate code and/or promote code reuse, instead of in the decomposition of the original problem. In this paper we propose a problem decomposition strategy that allows the use of a GP search to find solutions for subproblems and combine the individual solutions into the complete solution to the problem
Limit curve theorems in Lorentzian geometry
The subject of limit curve theorems in Lorentzian geometry is reviewed. A
general limit curve theorem is formulated which includes the case of converging
curves with endpoints and the case in which the limit points assigned since the
beginning are one, two or at most denumerable. Some applications are
considered. It is proved that in chronological spacetimes, strong causality is
either everywhere verified or everywhere violated on maximizing lightlike
segments with open domain. As a consequence, if in a chronological spacetime
two distinct lightlike lines intersect each other then strong causality holds
at their points. Finally, it is proved that two distinct components of the
chronology violating set have disjoint closures or there is a lightlike line
passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio
Painleve-Gullstrand Coordinates for the Kerr Solution
We construct a coordinate system for the Kerr solution, based on the zero
angular momentum observers dropped from infinity, which generalizes the
Painleve-Gullstrand coordinate system for the Schwarzschild solution. The Kerr
metric can then be interpreted as describing space flowing on a (curved)
Riemannian 3-manifold. The stationary limit arises as the set of points on this
manifold where the speed of the flow equals the speed of light, and the
horizons as the set of points where the radial speed equals the speed of light.
A deeper analysis of what is meant by the flow of space reveals that the
acceleration of free-falling objects is generally not in the direction of this
flow. Finally, we compare the new coordinate system with the closely related
Doran coordinate system.Comment: 6 pages; v2: new section, matches final published version; v3: sign
error in the expression of the function delta correcte
Spacelike surfaces with free boundary in the Lorentz-Minkowski space
We investigate a variational problem in the Lorentz-Minkowski space \l^3
whose critical points are spacelike surfaces with constant mean curvature and
making constant contact angle with a given support surface along its common
boundary. We show that if the support surface is a pseudosphere, then the
surface is a planar disc or a hyperbolic cap. We also study the problem of
spacelike hypersurfaces with free boundary in the higher dimensional
Lorentz-Minkowski space \l^{n+1}.Comment: 16 pages. Accepted in Classical and Quantum Gravit
Integration of the Friedmann equation for universes of arbitrary complexity
An explicit and complete set of constants of the motion are constructed
algorithmically for Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) models
consisting of an arbitrary number of non-interacting species. The inheritance
of constants of the motion from simpler models as more species are added is
stressed. It is then argued that all FLRW models admit what amounts to a unique
candidate for a gravitational epoch function (a dimensionless scalar invariant
derivable from the Riemann tensor without differentiation which is monotone
throughout the evolution of the universe). The same relations that lead to the
construction of constants of the motion allow an explicit evaluation of this
function. In the simplest of all models, the CDM model, it is shown
that the epoch function exists for all models with , but for
almost no models with .Comment: Final form to appear in Physical Review D1
The sectional curvature remains positive when taking quotients by certain nonfree actions
We study some cases when the sectional curvature remains positive under the
taking of quotients by certain nonfree isometric actions of Lie groups. We
consider the actions of the groups and such that the quotient space
can be endowed with a smooth structure using the fibrations
and . We prove that the quotient space
carries a metric of positive sectional curvature, provided that the original
metric has positive sectional curvature on all 2-planes orthogonal to the
orbits of the action.Comment: 26 pages, 1 figure. Changed the spelling of the author's nam
Non-interference for deterministic interactive programs
We consider the problem of defining an appropriate notion of non-interference (NI) for deterministic interactive programs. Previous work on the security of interactive programs by O'Neill, Clarkson and Chong (CSFW 2006) builds on earlier ideas due to Wittbold and Johnson (Symposium on Security and Privacy 1990), and argues for a notion of NI defined in terms of strategies modelling the behaviour of users. We show that, for deterministic interactive programs, it is not necessary to consider strategies and that a simple stream model of the users' behaviour is sufficient. The key technical result is that, for deterministic programs, stream-based NI implies the apparently more general strategy-based NI (in fact we consider a wider class of strategies than those of O'Neill et al). We give our results in terms of a simple notion of Input-Output Labelled Transition System, thus allowing application of the results to a large class of deterministic interactive programming languages
Computability of the causal boundary by using isocausality
Recently, a new viewpoint on the classical c-boundary in Mathematical
Relativity has been developed, the relations of this boundary with the
conformal one and other classical boundaries have been analyzed, and its
computation in some classes of spacetimes, as the standard stationary ones, has
been carried out.
In the present paper, we consider the notion of isocausality given by
Garc\'ia-Parrado and Senovilla, and introduce a framework to carry out
isocausal comparisons with standard stationary spacetimes. As a consequence,
the qualitative behavior of the c-boundary (at the three levels: point set,
chronology and topology) of a wide class of spacetimes, is obtained.Comment: 44 pages, 5 Figures, latex. Version with minor changes and the
inclusion of Figure
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